The title is a bit messed up, but I hope you understand what I mean. I've always been curious how we would look at the Romans if they weren't portrayed as living around 1 AD (i.e. "beginning of time"). Would they relate more to them, and see the similarities with the Middle Ages better? How would a Chinese calender translate to important (European and non-European) historical milestones?
I don't usually answer here, but I have a passing interest in calendars and the (conceptual) devices we use to keep track of time
On the Chinese calendar, we're currently in the year 4715 (with its new year usually occurring about early February), and the Hebrew calendar is currently nearing the end of the year 5775 (its new year begins in what is usually about mid-september). They're both "lunisolar" calendars, which is why their dates tend to drift against the Gregorian calendar, which is strictly a solar calendar. (They both have observed that there are sometimes 12 lunar rotations in a solar year, and sometimes 13)
So, using the older of the two, that moves your question back to about 3760 BC(E) and instead asking about what calendar may have come before that. But this begins pushing against what we believe to be the historical roots of civilizations on Earth, which we believe began emerging about 10,000 to 6,000 years ago. Before civilization, we didn't really have calendars. Calendars at their most basic were something we needed to make sure we planted our crops at the right times, and in the right seasons. But before agriculture (which is the what many draw as the distinctive line between uncivilized and civilized) you probably wouldn't have had much use for a calendar, nor the inclination to devise one.
You might also look into the Maya calendar, or the Celtic calendar, which also are both lunisolar, and also come from ancient civilizations, but unlike the Chinese and Hebrew calendars, they're not really still in use by people today.